Phase-locked loop（PLL） is commonly used in doubly-fed induction generator（DFIG） for its grid synchronization by tracking the phase angle of turbine terminal voltage; however a DFIG which is connected to weak grids by a synchronization technique will lead to instability. Consequently

we try to uncover the mechanism of phenomenon of instability. In non-ideal grid connection

terminal voltage phase angel is affected by the power outputs of DFIG

resulting in a dynamic coupling between PLL and DFIG power controls. Considering such a coupling effect

we propose a reduced small-signal model for a single DFIG infinite bus system. Based on this model

it is found that

owing to the coupling relation within active power and terminal voltage magnitude

an addition positive feedback branch is introduced to the PLL

and the loop gain increases as the system strength decreases

thus the stability of DFIG under weak grid operating conditions is deteriorated. Moreover

for open-loop terminal voltage control condition

the stability margin is analytically derived. Furthermore

the impact of terminal voltage control is also qualitatively analyzed. Full-order time-domain simulations are conducted to verify the effectiveness of the proposed simplified model and correlated analysis.